Complex Stochastic Gradient Descent and Directional Bias in Reproducing Kernel Hilbert Spaces
arXiv:2604.23017v2 Announce Type: replace Abstract: Stochastic Gradient Descent (SGD) is a known stochastic iterative method popular for large-scale convex optimization problems due to its simple implementation and scalability. Some objectives, such as those found in complex-valued neural networks, benefit from updates like in SGD and Gradient Descent (GD) with a newly defined ``gradient'' that allows for complex parameters. This complex variant of the SGD/GD methods has already been proposed, but convergence guarantees without analyticity constraints have not yet been provided. We propose a v
The paper addresses a long-standing theoretical gap in the convergence guarantees of complex stochastic gradient descent, a method relevant to emerging AI architectures.
Improved mathematical guarantees for complex SGD can accelerate research and development in complex-valued neural networks, potentially leading to more efficient or capable AI systems.
The theoretical foundation for complex-valued neural networks is strengthened, allowing for more robust development without previous analytical constraints.
- · AI researchers
- · Machine learning framework developers
- · Companies utilizing complex-valued neural networks
- · None
The immediate effect is a more solid theoretical base for complex-valued neural networks.
This could lead to a broader adoption and development of complex-valued AI models across various applications.
More efficient or novel AI models, enabled by these advancements, could contribute to overall AI progress and capability.
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Read at arXiv cs.LG